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Condensation transition and ensemble inequivalence in the discrete nonlinear Schrödinger equation

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Abstract

The thermodynamics of the discrete nonlinear Schrödinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a thermalized phase and a condensed (localized) one occurs at the infinite-temperature line. Inequivalence between statistical ensembles characterizes the condensed phase, where the grand-canonical representation does not apply. The control over finite-size corrections of the microcanonical partition function allows to design an experimental test of delocalized negative-temperature states in lattices of cold atoms.

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Acknowledgements

We thank for interesting discussions M. Baiesi, S. Franz, L. Leuzzi, G. Parisi, P. Politi, F. Ricci-Tersenghi, L. Salasnich, A. Scardicchio, F. Seno and A. Vulpiani. G.G. acknowledges the financial support of the Simons Foundation (Grant No. 454949, Giorgio Parisi) and the hospitality of “Sapienza”, University of Rome, for the first stages of this work. S.I. acknowledges support from Progetto di Ricerca Dipartimentale BIRD173122/17 of the University of Padova. R.L. acknowledges partial support from project MIUR-PRIN2017 Coarse-grained description for non-equilibrium systems and transport phenomena (CO- NEST) n. 201798CZL.

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Authors and Affiliations

  1. Gran Sasso Science Institute, Viale F. Crispi 7, 67100, L’Aquila, Italy

    Giacomo Gradenigo

  2. Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019, Sesto Fiorentino, Italy

    Stefano Iubini & Roberto Livi

  3. Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Italy

    Stefano Iubini & Roberto Livi

  4. Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Italy

    Roberto Livi

  5. LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405, Orsay, France

    Satya N. Majumdar

Authors
  1. Giacomo Gradenigo
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  2. Stefano Iubini
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  3. Roberto Livi
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  4. Satya N. Majumdar
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All authors equally contributed to the work.

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Correspondence to Giacomo Gradenigo.

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Gradenigo, G., Iubini, S., Livi, R. et al. Condensation transition and ensemble inequivalence in the discrete nonlinear Schrödinger equation. Eur. Phys. J. E 44, 29 (2021). https://doi.org/10.1140/epje/s10189-021-00046-5

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  • DOI: https://doi.org/10.1140/epje/s10189-021-00046-5

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